Question

A base of a prism is a trapezoid that has one base length of 4 in., another base length of 10 in., and a height of 4 in. The height of the prism is 10 in. Which of the following correctly calculates the area of the prism with a trapezoid base?(1 point)

Responses

300 in2
300 in. squared

220 in2
220 in. squared

280 in2
280 in. squared

432 in2

Answer 1

[AI-generated answer — Bot GPT 3.5]

The correct answer is 220 in2 or 220 in. squared.

To calculate the area of the trapezoid base of the prism, you can use the formula for the area of a trapezoid: A = 1/2 * (b1 + b2) * h, where b1 and b2 are the two base lengths and h is the height of the trapezoid.

In this case, the area of the trapezoid base is A = 1/2 * (4 + 10) * 4 = 1/2 * 14 * 4 = 28 * 2 = 56.

To find the total surface area of the prism, you need to add the lateral area and the area of the two bases. The lateral area is the perimeter of the trapezoid base multiplied by the height of the prism. The perimeter of the trapezoid is 4 + 10 + 4 + 4 = 22. Therefore, the lateral area is 22 * 10 = 220.

Finally, you add the area of the two bases (2 * 56) and the lateral area (220) to find the total surface area: 2 * 56 + 220 = 112 + 220 = 332.

Therefore, the correct answer is 220 in2 or 220 in. squared.